An electric power plant that would make use of the...

An electric power plant that would make use of the temperature gradient in the ocean has been proposed. The system is to operate between $20.0^{\circ} \mathrm{C}$ (surface-water temperature $)$ and $5.00^{\circ} \mathrm{C}$ (water temperature at a depth of about 1 $\mathrm{km}) \cdot(\mathrm{a})$ What is the maximum efficiency of such a system? (b) If the electric power output of the plant is $75.0 \mathrm{MW}$, how much energy is taken in from the warm reservoir per hour? (c) In view of your answer to part (a), explain whether you think such a system is worthwhile. Note that the "fuel" is free.

An electric power plant that would make use of the temperature gradient in the ocean has been proposed. The system is to operate between $20.0^{\circ} \mathrm{C}$ (surface-water temperature $)$ and $5.00^{\circ} \mathrm{C}$ (water temperature at a depth of about 1 $\mathrm{km}) \cdot(\mathrm{a})$ What is the maximum efficiency of such a system?
(b) If the electric power output of the plant is $75.0 \mathrm{MW}$, how much energy is taken in from the warm reservoir per hour?
(c) In view of your answer to part (a), explain whether you think such a system is worthwhile. Note that the "fuel" is free.

Key Concepts

Heat Engine Operation

The concept of a heat engine is fundamental to understanding the conversion of thermal energy into mechanical work or electrical energy. A heat engine operates by absorbing energy from a high-temperature reservoir, converting part of it into work, and discharging the remaining energy to a low-temperature reservoir.

Energy Conversion Analysis

This involves quantifying the relationship between input energy and useful work output based on system efficiency. By applying efficiency equations, one can determine parameters such as the required heat input to sustain a specified power output, which is crucial in both theoretical assessments and practical implementations of energy conversion systems.

Temperature Scale Conversion

In thermodynamic calculations, it is essential to convert temperatures from Celsius or other relative scales to the Kelvin scale, as the absolute temperature values are required for accurately applying formulas such as the Carnot efficiency equation and for ensuring the validity of energy balance calculations.

Carnot Efficiency

Carnot efficiency represents the theoretical maximum efficiency that any heat engine can achieve when operating between two thermal reservoirs. It is determined by the temperatures of the hot and cold reservoirs, both measured on an absolute (Kelvin) scale, and establishes an upper limit for energy conversion processes dictated by the laws of thermodynamics.

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